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effect of constituent behaviors (cf. Wimsatt, 1986, 1997; Bechtel & Richardson,
1993). The behavior of ideal gases satisfies this condition insofar as we are
interested in explaining such things as the Boyle-Charles law. So, for example,
in ideal gases the pressure on a container is simply the sum of the molecular
momenta conveyed to the container, and the temperature becomes the mean
molecular kinetic energy. These are simple aggregative conditions.
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Genes are
likewise sometimes treated as if their effects are largely or wholly additive,
though this is certainly a misrepresentation of the usual case (cf. Wimsatt, 1980).
Organization and interaction are the rules rather than the exception among genes.
To take the opposite extreme, Stuart Kauffman (1993) has focused on the role
that organization plays in understanding what he calls the 'origins of order'. In
Kauffman's models, the constituents are treated as simple Boolean switches; he
manages to extract a variety of surprising systemic effects from simple models
whose only constituents are these Boolean switches and with randomly assigned
connections. This is, as he says, 'order for free'. The result is a continuum of
cases, depending on the extent to which interactions determine systemic behav-
ior. At the extreme, represented by Kauffman, there is a sense in which the
systemic behavior can be thought of as emergent, and contrary to reductionism,
though still mechanistic (cf. Bechtel & Richardson, 1993).
The second constraint on reductionism is that there be a principled characteriza-
tion of the behavior of constituents based on the lower level theory alone. There are
many cases illustrating this constraint. One of the paradigms for interlevel reduc-
tion, the case of thermodynamics and statistical mechanics, illustrates the point
precisely. In the 1860s, there was a movement toward understanding thermody-
namics in terms of the kinetics of molecules.Maxwell was critical in this period, for
the first time suggesting that the kinetic theory should be understood in a statistical
or probabilistic form. Boltzmann took up the problems surrounding equilibrium
distributions in the 1860s and nonequilibrium cases in the early 1870s. The
mechanistic account they offered was often not well-received. One problem
they confronted concerned what is called irreversibility, from J. Loschmidt in
the middle of the decade. Newtonian mechanics (and for that matter, Quan-
tum Mechanics) shows no temporal bias. With reversed motion, any process
can be reversed without violating any dynamical principles. The second law of
Thermodynamics requires a temporal direction, as Boltzmann acknowledged.
The solution was probabilistic: the flow of heat from one source to a sink is
the transfer of kinetic energy, and the most likely transition is from lower to
higher entropy. Even if every microstate has the same probability, macrostates
are associated with varying numbers of microstates; the most likely macrostates
turn out to correspond to more frequent microstates. So the transition toward
greater entropy is simultaneously a transition toward more frequent microstates.
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Historically, it was precisely because gases are
dis
organized that they were the focus for statistical mechanics.
